Update in case anyone tries this in the future:
First 5 gallons, where I bottle-primed and added 1 packet of yeast is carbing, but pretty unevenly. Maybe half the bottles are close to fully carbed, and the other half still have a ways to go.
The 10 gallons I bottled after that, I followed the bottle priming dosage instructions for the yeast (20g/Hl or 10g/5gal, IIRC), and I batch-primed. Every three or four bottles I filled, I stirred the bottling bucket with a long spoon to rouse the yeast and keep the sugar solution mixed evenly. Those have all carbed up pretty well and evenly.
A few of the first batch I bottled have started leaking very slowly at the crown. I used my bench capper to try to pinch the crown on, and that's worked for some of them, but a few I couldn't get to seal.
Any thoughts on the leaky bottles? I thought about chilling them and riddling, but I'm worried about turning the bottles upside down if they're leaking. I think once they're chilled, though, the pressure will be a lot lower so maybe they won't leak?